Question

write the slope - intercept form of the equation with the given point and slope. through (1,5) and m = 3. y = 3x+2 y = 2x+3 y = 3x - 2

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m = 3$, the equation becomes $y=3x + b$.

Step2: Substitute the point

Substitute the point $(1,5)$ into the equation $y = 3x + b$. So, $5=3\times1 + b$.

Step3: Solve for $b$

Simplify the right - hand side: $5 = 3 + b$. Subtract 3 from both sides: $b=5 - 3=2$.

Step4: Write the final equation

The equation of the line in slope - intercept form is $y = 3x+2$.

Answer:

$y = 3x + 2$